5t/4=45/2<br><br>stuck on this one

Find the complex zeros of <br><img src="https://tex.z-dn.net/?f=%20f%28x%29%20%3D%20%7Bx%7D%5E%7B3%20%7D%20%20-%2013%20%7Bx%7D%5

timama [110]

$f(x) = 0 \\\\\implies x^3-13x^2+59x -87 =0\\\\\implies x^3 -3x^2 -10x^2 +30x +29x - 87=0\\\\\implies x^2(x-3) - 10x(x-3) + 29(x-3) =0\\\\\implies (x-3)(x^2 -10x +29) =0\\\\\implies x - 3 = 0 ~~ \text{or}~~x^2 -10x +29 = 0\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{-(-10) \pm \sqrt{(-10)^2 -4 \cdot 1 \cdot 29}}{2(1)}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm \sqrt{-16}}{2}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm 4i }{2}\\$

$\\\implies x =3~~ \text{ or} ~~ x =5 \pm 2i\\\\\text{Hence the complex roots are,}~ 5- 2i ~~ \text{and} ~~5 + 2i$

6 0

2 years ago

Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of 30 square feet. How long can

gregori [183]

It can be at least 5.4 feet long since the area of a square is A=s^2. 5.4 times 5.4 is 30

6 0

3 years ago

A triangle has a side lengths of 3 centimeters, 5 centimeters, and 4 centimeters. Abe used converse of the Pythagorean Theorem t

fgiga [73]

No, Abe is incorrect.

If you don’t know which side is the hypotenuse, you have to try every possibility.

3^ + 4^ = 5^
25 = 25

The triangle is a right triangle. The side which is 5 cm long is the hypotenuse.

8 0

2 years ago

Find the linearization L(x) of the function at a. f(x) = x^4 + 2x^2, a = 1

gregori [183]

The equation of the tangent line at x=1 can be written in point-slope form as

... L(x) = f'(1)(x -1) +f(1)

The derivative is ...

... f'(x) = 4x^3 +4x

so the slope of the tangent line is f'(1) = 4+4 = 8.

The value of the function at x=1 is

... f(1) = 1^4 +2·1^2 = 3

So, your linearization is ...